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A numerical study of bounds in the correlations of fractional quantum Hall states
by Prashant Kumar, F. D. M. Haldane
Submission summary
| Authors (as registered SciPost users): | Prashant Kumar |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2304.14991v4 (pdf) |
| Date accepted: | 2024-04-12 |
| Date submitted: | 2024-03-05 20:07 |
| Submitted by: | Kumar, Prashant |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We numerically compute the guiding center static structure factor $\bar S(\bf k)$ of various fractional quantum Hall (FQH) states to $\mathcal{O}\left((k\ell)^6\right)$ where $k$ is the wavenumber and $\ell$ is the magnetic length. Employing density matrix renormalization group on an infinite cylinder of circumference $L_y$, we study the two-dimensional limit using $L_y/\xi \gg 1$, where $\xi$ is the correlation length. The main findings of our work are: 1) the ground states that deviate away from the ideal conformal block wavefunctions, do not saturate the Haldane bound, and 2) the coefficient of $O\left((k\ell)^6\right)$ term appears to be bounded above by a value predicted by field theories proposed in the literature. The first finding implies that the graviton mode is not maximally chiral for experimentally relevant FQH states.
List of changes
1. We have clarified throughout the manuscript that rotational invariance is not a requirement for the existence of Haldane bound but it is a necessary condition for the saturation. Therefore, the preliminary sections discuss the properties of static structure factor without the assumption of rotational invariance. In the later sections, where we investigate the conditions for saturation of the bound, we specialize to the rotationally invariant case.
2. We have added discussion motivating the usage of composite-boson formulation in the manuscript.
3. Behavior of various physical quantities under Particle-Hole symmetry has been emphasized in section IV.
4. In the discussion section, we have commented on the experimental relevance of our numerical calculations. In particular, by utilizing the spectral sum rules of Golkar \textit{et al}, we can predict the relative spectral weights of spin $+2$ and $-2$ graviton excitations of FQH states. We demonstrate this via an explicit prediction for $\nu=1/3$. Further, we have added more discussions of the results obtained in section V as suggested by the referees.
5. Appendix C has been added reinterpreting the spectral sum rules of Golkar \textit{et al} in the guiding center formulation adopted in the manuscript.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report
The authors have revised their manuscript according to my criticism in a globally satisfactory manner and, as far as I can see, also to that of the other referees. I recommend publication, but I would invite the authors to consider two minor (technical) points prior to publication.
1) Reference [24] does not contain an arXiv number. If it has already been posted on the arXiv, please add the reference, or brand it as "unpublished" otherwise.
2) In the paragraph below Eq. (5), the quantum numbers $\alpha$ and $\beta$ in the quantum states, presumably associated with the guiding-center operators, are undefined. Please add a definition so that the reader may appreciate better the argument developed in the paragraph.
plus a little typo:
In the last paragraph of Sec. III, second sentence, the authors may correct to "degrees of freedom" and not "off".